Product formula of vectors
The vector a=(x 1, y 1) and the vector b=(x2, y2).
Ab = x1x 2+y1y2 = | a || b | cos θ (θ is the angle between a and b).
PS: Vector is not called "product", but called quantity product ... For example, A and B are called the product of quantity of A and B or point A multiplied by B.
Cross product formula
Cross product | c | =| a× b | =| a ||| b | sin
Vector multiplication is divided into inner product and outer product.
The inner product ab= 丨丨丨丨丨丨丨丨丨丨丨丨丨丨丨丨丨丨丨 (the inner product has no direction and is called point multiplication).
The outer product a× b = a b sin α (the outer product has a direction, which is called× multiplication), that is, the difference multiplication means convenience, so the difference is used.
In addition, the outer product can represent the area of a parallelogram with side lengths a and b.
= product of modules of two vectors ×cos included angle
= abscissa product+ordinate product
Extended data
The definition of vector is a basic concept in mathematics, physics, engineering science and many other natural sciences. Refers to a geometric object that has both size and direction and satisfies the parallelogram law.
The product of two vectors (inner product, dot product) is a quantity (undirected), which is denoted as a B. The coordinate of the product of one vector is expressed as a b = x x'+y y'.
The cross product (outer product, cross product) of two vectors A and B is a vector, denoted as a×b (here × "is not a multiplication symbol, but a representation method, which is different from" ∧ "). If a and b are not * * * lines, the modulus of a×b is: ∣ A× B ∣ = | A || B | SIN < A, b >；; The direction of a×b is perpendicular to A and B, and A, B and a×b form a right-handed system in this order. If A and B are vertical, then ∣a×b∣=|a|*|b|
In physics and engineering, geometric vectors are more often called vectors. Many physical quantities are vectors, such as the displacement of an object, the force exerted on it by a ball hitting a wall and so on. On the contrary, it is scalar, that is, a quantity with only size and no direction. Some definitions related to vectors are also closely related to physical concepts. For example, vector potential corresponds to potential energy in physics.
The concept of geometric vector is abstracted in linear algebra, and a more general concept of vector is obtained. Here, a vector is defined as an element of a vector space. It should be noted that these abstract vectors are not necessarily represented by number pairs, and the concepts of size and direction are not necessarily applicable. Therefore, when reading on weekdays, we need to distinguish the concept of "vector" according to the context. However, we can still find the basis of a vector space to set the coordinate system, and we can also define the norm and inner product on the vector space by choosing a suitable definition, which enables us to compare abstract vectors with specific geometric vectors.